Paper · Oct 28, 2026
The Yang-Mills flow in vector bundles over higher dimensional Riemannian manifolds
As on arXiv
Abstract
We develop a parabolic formulation of the Uhlenbeck gauge fixing theorem and use it to prove the maximal existence of the Yang-Mills flow in vector bundles over compact -dimensional Riemannian manifolds for . We apply Moser's iteration technique to give a new proof of the bound of the curvature. Using an idea of Hamilton on the Ricci flow, we also provide a new proof on uniform estimates of higher order derivatives. Furthermore, we investigate the blow-up of the Yang-Mills flow at the maximal existence time and improve an asymptotical result of Hong-Tian.
- Submitted
- Oct 28, 2026
- Subjects
- math.DG
Comments: This replaces Hong's paper arxiv.org/abs/1701.00601
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.4Blow-Ups, Blow-Downs and Splitting at Infinity
Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.
- 11B.6Rotationally Symmetric Flows and the Standard Solution
The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.
- 6A.13Self-Similar Variables and Monotonicity
Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.